The original way to train such SOM is with Kohonen's iterations. Despite its
simplicity, they require a time dependant neighborhood function whose
neighborhood radius (or temperature) strictly decreases towards zero during
training. In [1]} and [2]}, heuristics are proposed
in a non-probabilistic framework to adapt this temperature. They lead to
“dynamic” SOM algorithms that are able to track non-stationary datasets. In
[3]}, the variational EM framework is used to design a cost
function for the SOM but the temperature parameter is still decreased as in
Kohonen. In [4]}, the topologically preserving properties of the
map stems from the basis function regularity. Hence those basis functions have
to be carefully chosen and their number must typically grow exponentially with
the observation space dimension.
